This paper presents a new analytical method to design fractional-order proportional–integral–derivative (PID) controllers. The control parameters are calculated so that the closed-loop system approximates a desired transfer function with transient response requirements. This function is determined based on the characteristic ratio assignment method. The control parameters are calculated by matching the first three moments of the closed-loop transfer function with the corresponding values of the desired system. Furthermore, to ensure closed-loop stability the proposed method is improved by using the shifted moments around the crossover frequency. Illustrative examples are given to show the performance of the proposed method.
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